By way of background, Von Hamos and Hall's spectrometers have been used in the past at laser facilities. FIG. 1 depicts the geometry of the von Hamos spectrometer. The source and its images for different Bragg angles θ are on the cylinder axis, an axis of rotational symmetry. The imaging equation is 1/p+1/q=2 sin (θ)/R.
Hall's ‘single-cone’ crystal spectrometer design was introduced in 1984 and has become the standard x-ray crystal spectrometer for time-resolved spectral measurements at the National Ignition Facility (NIF) in Livermore, the Omega Laser Facility in Rochester, and other laser facilities. FIG. 2 depicts the geometry of Hall's conical crystal spectrograph. The imaging equation is still valid for all Bragg angles, although this spectrograph instrument, as provided herein. In Hall's spectrometer the ray patterns do not have rotational symmetry And since this is a basic requirement for accurate imaging, Hall's spectrometer violates basic Physics laws. As a result, (a) the spectral resolution of hall's spectrometer is not even defined; and (b) large imaging errors occur as the size of the crystal, which is the x-ray reflecting and x-ray focusing element of an x-ray spectrometer, is increased. The size of the x-ray reflecting area in Hall's spectrometer is therefore small, typically only 2 cm×3 cm. On the other hand, the photon throughput (light intensity) is proportional to the size of the crystal, so that in Hall's spectrometer the photon throughput is limited by the small crystal size.
The source and its images for different Bragg angles θ are on the cylinder axis, an axis of rotational symmetry, so that the Hall's spectrometer the ray patterns do not have rotational symmetry And since this is a basic requirement for accurate imaging, Hall spectrometer violates basic Physics laws. As a result, (a) the spectral resolution of hall's spectrometer is not even defined; and (b) large imaging errors occur as the size of the crystal, which is the x-ray reflecting and x-ray focusing element of an x-ray spectrometer, is increased. The size of the x-ray reflecting area in Hall's spectrometer is therefore small, typically only 2 cm×3 cm. On the other hand, the photon throughput (light intensity) is proportional to the size of the crystal, so that in Hall's spectrometer the photon throughput is limited by the small crystal size. This instrument is deeply flawed due to the fact that the source is NOT on an axis of rotational symmetry. Hall's spectrometer is therefore not an imaging spectrometer and its spectral resolution is not even defined.
There is a need for an x-ray imaging spectrometer with a well-defined spectral resolution for a selectable, i.e., arbitrary, range of Bragg angles as noted in the Appendix.